Project P1
IE 423 Quality Engineering
Project Part 1
GROUP 6
Part 1.1
library("jpeg", lib.loc="C:/Program Files/R/R-3.4.4/library")
img <- readJPEG("C:/Trial7.jpeg")
str(img)## num [1:512, 1:512, 1:3] 0.741 0.702 0.655 0.635 0.663 ...Part 1.2
dim(img)## [1] 512 512 3Part 1.2.a
plot(0:512+0.5, 0:512+0.5, type="n", asp=1)
rasterImage(img, 0.5, 0.5, 512.5, 512.5,interpolate=FALSE)
Part 1.2.b
splitimg <- img
plot(0:512+0.5, 0:512+0.5, type="n", asp=1)
splitimg[,,] <- 0
splitimg[,,1] <- img[,,1]
rasterImage(splitimg[,,], 0.5, 0.5, 512.5, 512.5,interpolate=FALSE)
plot(0:512+0.5, 0:512+0.5, type="n", asp=1)
splitimg[,,] <- 0
splitimg[,,2] <- img[,,2]
rasterImage(splitimg[,,], 0.5, 0.5, 512.5, 512.5,interpolate=FALSE)
plot(0:512+0.5, 0:512+0.5, type="n", asp=1)
splitimg[,,] <- 0
splitimg[,,3] <- img[,,3]
rasterImage(splitimg[,,], 0.5, 0.5, 512.5, 512.5,interpolate=FALSE)
Part 1.3
chan1<-1:512
chan2<-1:512
chan3<-1:512
for(i in 1:512)
chan1[i]<-mean(img[,i,1])
for(i in 1:512)
chan2[i]<-mean(img[,i,2])
for(i in 1:512)
chan3[i]<-mean(img[,i,3])
par(mfrow=c(2,2))
plot(chan1,type="l", col="red")
plot(chan2,type="l", col="green")
plot(chan2,type="l", col="blue")
Part 1.4
normalize <- function(x) {
return ((x - min(x)) / (max(x) - min(x)))
}
d2 <- matrix(1, 512, 256)
for (i in 1:512)
{
for (j in 1:256)
{
d2[i, j] <- img[i, j, 1]
}
}
d3 <- matrix(1, 512, 256)
for (i in 1:512)
{
for (j in 1:256)
{
d3[i, j] <- img[i, j + 256, 1]
}
}
d5 <- matrix(1, 512, 256)
for (i in 1:512)
{
for (j in 1:256)
{
d5[i, j] <- d3[i, j] - d2[i, j]
}
}
d6 <- matrix(1, 512, 256)
d6 <- normalize(d5)
plot(0:512 + 0.5, 0:512 + 0.5, type = "n", asp=1)
splitimg[, , ] <- 0
splitimg[, , 1] <- d6[, ]
rasterImage(splitimg[,1:256,], 0.5, 0.5, 256.5, 512.5, interpolate = FALSE)
c2 <- matrix(1, 512, 256)
for (i in 1:512)
{
for (j in 1:256)
{
c2[i, j] <- img[i, j, 2]
}
}
c3 <- matrix(1, 512, 256)
for (i in 1:512)
{
for (j in 1:256)
{
c3[i, j] <- img[i, j + 256, 2]
}
}
c5 <- matrix(1, 512, 256)
for (i in 1:512)
{
for (j in 1:256)
{
c5[i, j] <- c3[i, j] - c2[i, j]
}
}
c6 <- matrix(1, 512, 256)
c6 <- normalize(c5)
plot(0:512 + 0.5, 0:512 + 0.5, type = "n", asp = 1)
splitimg[, , ] <- 0
splitimg[, , 2] <- c6[, ]
rasterImage(splitimg[,1:256,], 0.5, 0.5, 256.5, 512.5, interpolate = FALSE)
e2 <- matrix(1, 512, 256)
for (i in 1:512)
{
for (j in 1:256)
{
e2[i, j] <- img[i, j, 3]
}
}
e3 <- matrix(1, 512, 256)
for (i in 1:512)
{
for (j in 1:256)
{
e3[i, j] <- img[i, j + 256, 3]
}
}
e5 <- matrix(1, 512, 256)
for (i in 1:512)
{
for (j in 1:256)
{
e5[i, j] <- e3[i, j] - e2[i, j]
}
}
e6 <- matrix(1, 512, 256)
e6 <- normalize(e5)
plot(0:512 + 0.5, 0:512 + 0.5, type = "n", asp=1)
splitimg[, , ] <- 0
splitimg[, , 3] <- e6[, ]
rasterImage(splitimg[,1:256,], 0.5, 0.5, 256.5, 512.5, interpolate = FALSE)
Part 1.5
3x3 Median Filtering:
vec2 <- 1:9
newimage3 <- matrix(vec2, 3, 3)
uc1 <- img[, , 1]
for (i in 2:511)
{
for (j in 2:511)
{
for (k in 1:3)
{
for (l in 1:3)
{
newimage3[k, l] <- img[i + k - 2, j + l - 2, 1]
}
}
uc1[i, j] <- median(newimage3)
}
}
uc2 <- img[, , 2]
for (i in 2:511)
{
for (j in 2:511)
{
for (k in 1:3)
{
for (l in 1:3)
{
newimage3[k, l] <- img[i + k - 2, j + l - 2, 2]
}
}
uc2[i, j] <- median(newimage3)
}
}
uc3 <- img[, , 3]
for (i in 2:511)
{
for (j in 2:511)
{
for (k in 1:3)
{
for (l in 1:3)
{
newimage3[k, l] <- img[i + k - 2, j + l - 2, 3]
}
}
uc3[i, j] <- median(newimage3)
}
}
kaa <- array(1:786432, dim = c(512, 512, 3))
kaa[, , 1] <- uc1
kaa[, , 2] <- uc2
kaa[, , 3] <- uc3
plot(0:512 + 0.5, 0:512 + 0.5, type = "n", asp=1)
rasterImage(kaa, 0.5, 0.5, 512.5, 512.5, interpolate = FALSE)
5x5 Median Filtering:
vec1 <- 1:25
newimage5 <- matrix(vec1, 5, 5)
besebes1 <- img[, , 1]
for (i in 3:510)
{
for (j in 3:510)
{
for (k in 1:5)
{
for (l in 1:5)
{
newimage5[k, l] <- img[i + k - 3, j + l - 3, 1]
}
}
besebes1[i, j] <- median(newimage5)
}
}
besebes2 <- img[, , 2]
for (i in 3:510)
{
for (j in 3:510)
{
for (k in 1:5)
{
for (l in 1:5)
{
newimage5[k, l] <- img[i + k - 3, j + l - 3, 2]
}
}
besebes2[i, j] <- median(newimage5)
}
}
besebes3 <- img[, , 3]
for (i in 3:510)
{
for (j in 3:510)
{
for (k in 1:5)
{
for (l in 1:5)
{
newimage5[k, l] <- img[i + k - 3, j + l - 3, 3]
}
}
besebes3[i, j] <- median(newimage5)
}
}
aks <- array(1:786432, dim = c(512, 512, 3))
aks[, , 1] <- besebes1
aks[, , 2] <- besebes2
aks[, , 3] <- besebes3
plot(0:512 + 0.5, 0:512 + 0.5, type = "n", asp = 1)
rasterImage(aks, 0.5, 0.5, 512.5, 512.5, interpolate = FALSE)
11x11 Median Filtering:
vec3 <- 1:121
newimage11 <- matrix(vec3, 11, 11)
onbir1 <- img[, , 1]
for (i in 6:507)
{
for (j in 6:507)
{
for (k in 1:11)
{
for (l in 1:11)
{
newimage11[k, l] <- img[i + k - 6, j + l - 6, 1]
}
}
onbir1[i, j] <- median(newimage11)
}
}
onbir2 <- img[, , 2]
for (i in 6:507)
{
for (j in 6:507)
{
for (k in 1:11)
{
for (l in 1:11)
{
newimage11[k, l] <- img[i + k - 6, j + l - 6, 2]
}
}
onbir2[i, j] <- median(newimage11)
}
}
onbir3 <- img[, , 3]
for (i in 6:507)
{
for (j in 6:507)
{
for (k in 1:11)
{
for (l in 1:11)
{
newimage11[k, l] <- img[i + k - 6, j + l - 6, 3]
}
}
onbir3[i, j] <- median(newimage11)
}
}
caa <- array(1:786432, dim = c(512, 512, 3))
caa[, , 1] <- onbir1
caa[, , 2] <- onbir2
caa[, , 3] <- onbir3
plot(0:512 + 0.5, 0:512 + 0.5, type = "n", asp = 1)
rasterImage(caa, 0.5, 0.5, 512.5, 512.5, interpolate = FALSE)
31x31 Median Filtering:
vec4 <- 1:961
newimage31 <- matrix(vec4, 31, 31)
otuzbir1 <- img[, , 1]
for (i in 16:497)
{
for (j in 16:497)
{
for (k in 1:31)
{
for (l in 1:31)
{
newimage31[k, l] <- img[i + k - 16, j + l - 16, 1]
}
}
otuzbir1[i, j] <- median(newimage31)
}
}
otuzbir2 <- img[, , 2]
for (i in 16:497)
{
for (j in 16:497)
{
for (k in 1:31)
{
for (l in 1:31)
{
newimage31[k, l] <- img[i + k - 16, j + l - 16, 2]
}
}
otuzbir2[i, j] <- median(newimage31)
}
}
otuzbir3 <- img[, , 3]
for (i in 16:497)
{
for (j in 16:497)
{
for (k in 1:31)
{
for (l in 1:31)
{
newimage31[k, l] <- img[i + k - 16, j + l - 16, 3]
}
}
otuzbir3[i, j] <- median(newimage31)
}
}
faa <- array(1:786432, dim = c(512, 512, 3))
faa[, , 1] <- otuzbir1
faa[, , 2] <- otuzbir2
faa[, , 3] <- otuzbir3
plot(0:512 + 0.5, 0:512 + 0.5, type = "n", asp = 1)
rasterImage(faa, 0.5, 0.5, 512.5, 512.5, interpolate = FALSE)
The median filter technique is effective in removing the noise in the photograph, but it affects the edges negatively. However, it is important to protect the edges while reducing noise in a photograph. That’s why we chose a photo that would consist of too many edges. As shown in the examples, the edges are critical for its visual appearance. As the window size used in median filtering increases, the image will have smoother transitions and the edges will be adversely affected. Median filtering technique can give very good results in photographs with low edges and high spot noise
Part 2.1
library("imager", lib.loc="C:/Program Files/R/R-3.4.4/library")## Loading required package: magrittr##
## Attaching package: 'imager'## The following object is masked from 'package:magrittr':
##
## add## The following objects are masked from 'package:stats':
##
## convolve, spectrum## The following object is masked from 'package:graphics':
##
## frame## The following object is masked from 'package:base':
##
## save.imageimg <- readJPEG("C:/last.jpg")
img1<-as.cimg(img)## Warning in as.cimg.array(img): Assuming third dimension corresponds to
## colourimg <- grayscale(img1)
hist(img)
The distribution looks a lot like the normal distribution except for the fact that it is left skewed. But since the left tail of the distribution is not too long it is possible that normal distribution will be a good fit.
Part 2.2
imgold<-img
library("MASS", lib.loc="C:/Program Files/R/R-3.4.4/library")
fitdistr(imgold,"normal")## mean sd
## 6.157043e-01 6.356295e-02
## (1.241464e-04) (8.778475e-05)mean(imgold)## [1] 0.6157043sd(imgold)## [1] 0.06356307The mean and standard deviation of fit is close enough to the original mean and standard deviation. Thus, it is safe to say that the data (the pixel values of our image) follows a normal distribution.
Part 2.3
While calculating, we used the mean and standard deviation of the original image instead of the ones displayed above (the output of fitting the data) since the values are significantly close to each other.
upperlim<- qnorm(0.9995,mean(imgold),sd(imgold))
lowerlim<- qnorm(0.0005,mean(imgold),sd(imgold))
img[img<=lowerlim]=0
img[img>=upperlim]=0
plot(img)
plot(imgold)
The processed image has more dark points as expected. Since the original image was rather bright, changing outliers to black was very efficient in detecting the error in the image (thus,detecting the error in the fabric). If the image to be processed was an image with darker tones, we could have had a different result where the alteration made the image look more homogeneous (thus giving a false sense about the quality of the fabric).
Part 2.4
imgg<-grayscale(img1)
limits<- array(dim=c(10,10,2))
for(i in 1:10){
for(j in 1:10){
k<- 51*(j-1)+1
l<- 51*(i-1)+1
patch<- imgg[k:(k+50),l:(l+50),,]
upp<-qnorm(0.9995,mean(patch),sd(patch))
low<-qnorm(0.0005,mean(patch),sd(patch))
limits[j,i,1]<-low
limits[j,i,2]<-upp
}
}
for(k in 1:509){
for(l in 1:509){
w<- floor(k/51)+1
z<- floor(l/51)+1
if(imgg[k,l,,]<=limits[w,z,1]){
imgg[k,l,,]=0
}
if(imgg[k,l,,]>=limits[w,z,2]){
imgg[k,l,,]=0
}
}
}
imgfinal<-imgg
plot(imgfinal) 
plot(imgold)
Compared to the image we got in the previous question, this image seems less noisy. This might be because the evaluation for which pixel to be zeroed out gives different results when it is made in small scale. In the previous question all pixels were compared to one upper and lower limit. That option is a better option since the pixels values(thus the brightness and the darkness) of the image varies from one location to another. By comparing every pixel with one general value we may choose to zero out the pixels that actually blend in good locally, but are out of the boundary with respect to general limits. This results in a better quality control since we won’t miss any defects that are out of a certain quality measure. That is why setting local upper and lower limits for small patches is expected to give worse results. That is also what we observed in this part. Compared to the original image the image we obtained in this part seems a bit more smooth colorwise, and results in less marked (blackened) pixels, since the pixels are evaluated locally.